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Definition of implication : 1. An implying, or that which is implied, but not expressed; an inference, or something which may fairly be understood, though not expressed in words.
2. The act of implicating, or the state of being implicated.

Synonyms:

subtraction, association, intimation, insinuation, import, deductive reasoning, assumption, moment, tax write-off, conditional relation, suggest, connection, union, signification, tax deduction, suggestion, inkling, price reduction, suspicion, relationship, logical implication, undertone, innuendo, importee, importation, entanglement, entailment, hint, undercurrent, synthesis, consequence, involvement, guess, deduction, inference, show, discount

culpability, guilt, corruption, blameworthiness, incrimination, transgression, red-handedness

gist, tenor, definition, interpretation, intent, significance, explanation, denotation, relevance, connotation, point, meaning, pith, crux, upshot, thrust, purpose, topic, message, drift, description, subject, indication

count, writ, lawsuit, hearing, subpoena, case, accusation, impeachment, charge, action, indictment, allegation, citation, affidavit, prosecution, suit, summons, arraignment, litigation, grievance, complaint

Usage examples:

• That was as noble in him as the implication of Jack's whereabouts had been base. - "The Mysterious Rider", Zane Grey.
• Here he seemed to allow by implication for Peetka's prejudice- there were two kinds of pale- face strangers- and on an impulse he drew out Muckluck's medal. - "The Magnetic North", Elizabeth Robins (C. E. Raimond).
• In common speech, to deny a quality of anything is by implication to attribute to it some other quality of the same kind. - "Logic, Inductive and Deductive", William Minto.